Nuprl Lemma : member-empty-cubical-subset
∀[I:fset(ℕ)]. ∀[phi:Point(face_lattice(I))].
∀[X,A:Top]. (A ∈ {I,phi ⊢ _:X}) supposing phi = 0 ∈ Point(face_lattice(I))
Proof
Definitions occuring in Statement :
cubical-term: {X ⊢ _:A},
cubical-subset: I,psi,
face_lattice: face_lattice(I),
lattice-0: 0,
lattice-point: Point(l),
fset: fset(T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
bdd-distributive-lattice: BoundedDistributiveLattice,
so_lambda: λ2x.t[x],
and: P ∧ Q,
so_apply: x[s]
Lemmas referenced :
nat_wf,
fset_wf,
lattice-join_wf,
lattice-meet_wf,
uall_wf,
bounded-lattice-axioms_wf,
bounded-lattice-structure-subtype,
lattice-axioms_wf,
lattice-structure_wf,
bounded-lattice-structure_wf,
subtype_rel_set,
bdd-distributive-lattice_wf,
lattice-0_wf,
face_lattice_wf,
lattice-point_wf,
equal_wf,
top_wf,
empty-cubical-subset-term
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
independent_isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
applyEquality,
because_Cache,
lambdaEquality,
setElimination,
rename,
instantiate,
productEquality,
cumulativity,
universeEquality
Latex:
\mforall{}[I:fset(\mBbbN{})]. \mforall{}[phi:Point(face\_lattice(I))]. \mforall{}[X,A:Top]. (A \mmember{} \{I,phi \mvdash{} \_:X\}) supposing phi = 0
Date html generated:
2016_05_18-PM-01_58_16
Last ObjectModification:
2016_01_28-PM-01_23_59
Theory : cubical!type!theory
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